# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held on 12-4-2019 Afternoon)

### done JEE Main Online Paper (Held on 12-4-2019 Afternoon)

• question_answer1) The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${{\lambda }_{1}}/{{\lambda }_{2}},$of the photons emitted in this process is : [JEE Main 12-4-2019 Afternoon]

A) 9/7

B) 7/5

C) 27/5

D) 20/7

• question_answer2) One kg of water, at $20{}^\text{o}C,$is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20\Omega$. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to :

 [Specific heat of water $=4200\text{ }J/kg\text{ }{}^\text{o}C$), Latent heat of water = 2260 kJ/kg]
[JEE Main 12-4-2019 Afternoon]

A) 3 minutes

B) 22 minutes

C) 10 minutes

D) 16 minutes

• question_answer3) A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, ${{l}_{1}}=30cm$and ${{l}_{2}}=70cm$. Then n is equal to : [JEE Main 12-4-2019 Afternoon]

A) $332m{{s}^{-1}}$

B) $379m{{s}^{-1}}$

C) $384m{{s}^{-1}}$

D) $338m{{s}^{-1}}$

• question_answer4) Two sources of sound ${{S}_{1}}$ and ${{S}_{2}}$ produce sound waves of same frequency 660 Hz. A listener is moving from source ${{S}_{1}}$towards ${{S}_{2}}$ with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals: [JEE Main 12-4-2019 Afternoon]

A) 2.5 m/s

B) 15.0 m/s

C) 5.5 m/s

D) 10.0 m/s

• question_answer5) A particle is moving with speed $\text{v}\,\text{=}\,\text{b}\sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t=\tau$(assume that the particle is at origin at t = 0). [JEE Main 12-4-2019 Afternoon]

A) $\frac{{{b}^{2}}\tau }{4}$

B) $\frac{{{b}^{2}}\tau }{2}$

C) ${{b}^{2}}\tau$

D) $\frac{{{b}^{2}}\tau }{\sqrt{2}}$

• question_answer6) Consider an electron in a hydrogen atom, revolving in its second excited state (having radius $4.65\overset{\text{o}}{\mathop{\text{A}}}\,$). The de-Broglie wavelength of this electron is : [JEE Main 12-4-2019 Afternoon]

A) $12.9\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $3.5\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $9.7\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $6.6\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer7) A moving coil galvanometer, having a resistance G, produces full scale deflection when a current ${{I}_{g}}$flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to ${{I}_{0}}({{I}_{0}}>{{I}_{g}})$by connecting a shunt resistance ${{R}_{A}}$ to it and (ii) into a voltmeter of range 0 to $V(V=G{{I}_{0}})$ by connecting a series resistance ${{R}_{V}}$to it. Then, [JEE Main 12-4-2019 Afternoon]

A) ${{R}_{A}}{{R}_{V}}={{G}^{2}}\left( \frac{{{I}_{g}}}{{{I}_{0}}-{{I}_{g}}} \right)$and$\frac{{{R}_{A}}}{{{R}_{V}}}={{\left( \frac{{{I}_{0}}-{{I}_{g}}}{{{I}_{g}}} \right)}^{2}}$

B) ${{R}_{A}}{{R}_{V}}={{G}^{2}}$and$\frac{{{R}_{A}}}{{{R}_{V}}}={{\left( \frac{{{I}_{g}}}{{{I}_{0}}-{{I}_{g}}} \right)}^{2}}$

C) ${{R}_{A}}{{R}_{V}}={{G}^{2}}$and$\frac{{{R}_{A}}}{{{R}_{V}}}=\frac{{{I}_{g}}}{({{I}_{g}}-{{I}_{g}})}$

D) ${{R}_{A}}{{R}_{V}}={{G}^{2}}\left( \frac{{{I}_{0}}-{{I}_{g}}}{{{I}_{g}}} \right)$and$\frac{{{R}_{A}}}{{{R}_{V}}}={{\left( \frac{{{I}_{g}}}{{{I}_{0}}-{{I}_{g}}} \right)}^{2}}$

• question_answer8) The number density of molecules of a gas depends on their distance r from the origin as, $n(r)={{n}_{0}}{{e}^{-\alpha {{r}^{4}}}}.$Then the total number of molecules is proportional to : [JEE Main 12-4-2019 Afternoon]

A) ${{n}_{0}}{{\alpha }^{1/4}}$

B) ${{n}_{0}}{{\alpha }^{-3}}$

C) ${{n}_{0}}{{\alpha }^{-3/4}}$

D) $\sqrt{{{n}_{0}}}{{\alpha }^{1/2}}$

• question_answer9) A smooth wire of length $2\pi r$is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ${{\omega }^{2}}$ is equal to : [JEE Main 12-4-2019 Afternoon]

A) $\left( g\sqrt{3} \right)/r$

B) $\frac{\sqrt{3}g}{2r}$

C) $2g/r$

D) $2g/\left( r\sqrt{3} \right)$

• question_answer10) Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) [JEE Main 12-4-2019 Afternoon]

A) $3.0\times {{10}^{5}}T$

B) $2.5\times {{10}^{5}}T$

C) $2.0\times {{10}^{5}}T$

D) $1.5\times {{10}^{5}}T$

• question_answer11) A transparent cube of side d, made of a material of refractive index ${{\mu }_{2}},$is immersed in a liquid of refractive index ${{\mu }_{1}}({{\mu }_{1}}<{{\mu }_{2}}).$A ray is incident on the face AB at an angle $\theta$(shown in the figure). Total internal reflection takes place at point E on the face BC. The $\theta$ must satisfy: [JEE Main 12-4-2019 Afternoon]

A) $\theta <{{\sin }^{-1}}\frac{{{\mu }_{1}}}{{{\mu }_{2}}}$

B) $\theta <{{\sin }^{-1}}\sqrt{\frac{\mu _{2}^{2}}{\mu _{1}^{2}}-1}$

C) $\theta >{{\sin }^{-1}}\frac{{{\mu }_{1}}}{{{\mu }_{2}}}$

D) $\theta >{{\sin }^{-1}}\sqrt{\frac{\mu _{2}^{2}}{\mu _{1}^{2}}-1}$

• question_answer12) Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $\rho (r)=kr,$where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then: [JEE Main 12-4-2019 Afternoon]

A) $a=\frac{3R}{{{2}^{{}^{1}/{}_{4}}}}$

B) $a=R/\sqrt{3}$

C) $a={{8}^{-1/4}}R$

D) $a={{2}^{-1/4}}R$

• question_answer13) Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights,${{h}_{1}}$and ${{h}_{2}}.$Which of the following is correct ? [JEE Main 12-4-2019 Afternoon]

A) ${{R}^{2}}=2\,{{h}_{1}}{{h}_{2}}$

B) ${{R}^{2}}=16\,{{h}_{1}}{{h}_{2}}$

C) ${{R}^{2}}=4\,{{h}_{1}}{{h}_{2}}$

D) ${{R}^{2}}=\,{{h}_{1}}{{h}_{2}}$

• question_answer14) A spring whose unstretched length is $l$ has a force constant k. The spring is cut into two pieces of un stretched lengths ${{l}_{1}}$and ${{l}_{2}}$ where, ${{l}_{1}}=n{{l}_{2}}$and n is an integer. The ratio ${{k}_{1}}/{{k}_{2}}$of the corresponding force constants, ${{k}_{1}}$and ${{k}_{2}}$will be : [JEE Main 12-4-2019 Afternoon]

A) $\frac{1}{{{n}^{2}}}$

B) ${{n}^{2}}$

C) $\frac{1}{n}$

D) $n$

• question_answer15) A block of mass 5 kg is (i) pushed in case [A] and (ii) pulled in case , by a force F = 20 N, making an angle of $30{}^\text{o}$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu =0.2.$The difference between the accelerations of the block, in case [B] and case [A] will be : $(g=10m{{s}^{-2}})$ [JEE Main 12-4-2019 Afternoon]

A) $0m{{s}^{-2}}$

B) $0.8\,m{{s}^{-2}}$

C) $0.4\,m{{s}^{-2}}$

D) $3.2\,m{{s}^{-2}}$

• question_answer16) Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and $t=\frac{L}{R}$is [JEE Main 12-4-2019 Afternoon]

A) $\frac{EL}{7.3{{R}^{2}}}$

B) $\frac{EL}{2.7{{R}^{2}}}$

C) $\frac{7.3EL}{{{R}^{2}}}$

D) $\frac{2.7EL}{{{R}^{2}}}$

• question_answer17) A system of three polarizers ${{P}_{1}},{{P}_{2}},{{P}_{3}}$is set up such that the pass axis of${{P}_{3}}$is crossed with respect to that of ${{P}_{1}}$. The pass axis of ${{P}_{2}}$is inclined at $60{}^\text{o}$ to the pass axis of ${{P}_{3}}$. When a beam of unpolarized light of intensity ${{I}_{0}}$ is incident on ${{P}_{1}},$the intensity of light transmitted by the three polarizers is I. The ratio $({{I}_{0}}/I)$ equals (nearly) : [JEE Main 12-4-2019 Afternoon]

A) 16.00

B) 1.80

C) 5.33

D) 10.67

• question_answer18) Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be : [JEE Main 12-4-2019 Afternoon]

A) 9 : 8

B) 1 : 8

C) 8 : 1

D) 3 : 8

• question_answer19) A solid sphere, of radius R acquires a terminal velocity${{\text{v}}_{1}}$when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, ${{\text{v}}_{2}},$when falling through the same fluid, the ratio $\text{(}{{\text{v}}_{1}}/{{\text{v}}_{2}})$equals : [JEE Main 12-4-2019 Afternoon]

A) 1/27

B) 1/9

C) 27

D) 9

• question_answer20) The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9 : 4. The mass of the planet is$\frac{1}{9}$th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density) [JEE Main 12-4-2019 Afternoon]

A) $\frac{R}{3}$

B) $\frac{R}{2}$

C) $\frac{R}{4}$

D) $\frac{R}{9}$

• question_answer21) Figure shown a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6V. If the unregulated input voltage varies between 10 V to 16 V, then what is the maximum Zener current? [JEE Main 12-4-2019 Afternoon]

A) 2.5 mA

B) 3.5 Ma

C) 7.5 mA

D) 1.5 mA

• question_answer22) A Carnot engine has an efficiency of 1/6. When the temperature of the sink is reduced by $62{}^\text{o}C$, its efficiency is doubled. The temperatures of the source and the sink are, respectively [JEE Main 12-4-2019 Afternoon]

A) $124{}^\text{o}C,62{}^\text{o}C$

B) $37{}^\text{o}C,99{}^\text{o}C$

C) $62{}^\text{o}C,124{}^\text{o}C$

D) $99{}^\text{o}C,37{}^\text{o}C$

• question_answer23) A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process? [JEE Main 12-4-2019 Afternoon]

A) 35 J

B) 40 J

C) 25 J

D) 30 J

• question_answer24) A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as ${{10}^{-12}}W/{{m}^{2}}$] [JEE Main 12-4-2019 Afternoon]

A) 10 cm

B) 30 cm

C) 40 cm

D) 20 cm

• question_answer25) A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to : [JEE Main 12-4-2019 Afternoon]

A) $F/(3\pi {{r}^{2}}YT)$

B) $3F/(\pi {{r}^{2}}YT)$

C) $6F/(\pi {{r}^{2}}YT)$

D) $9F/(\pi {{r}^{2}}YT)$

• question_answer26) Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be : [JEE Main 12-4-2019 Afternoon]

A) $\left( \frac{7}{12}m,\frac{\sqrt{3}}{8}m \right)$

B) $\left( \frac{\sqrt{3}}{4}m,\frac{5}{12}m \right)$

C) $\left( \frac{7}{12}m,\frac{\sqrt{3}}{4}m \right)$

D) $\left( \frac{\sqrt{3}}{8}m,\frac{7}{12}m \right)$

• question_answer27) An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $\vec{B}=(1.5\times {{10}^{-3}}T)\hat{k}$at S (See figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is :

 (electron's charge $=1.6\times {{10}^{19}}C,$ mass of electron $=9.1\times {{10}^{31}}\text{ }kg$)
[JEE Main 12-4-2019 Afternoon]

A) 12.87 cm

B) 1.22 cm

C) 11.65 cm

D) 2.25 cm

• question_answer28) A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the electric field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave? [JEE Main 12-4-2019 Afternoon]

A) $\vec{B}=2\times {{10}^{7}}\sin (0.5\times {{10}^{3}}z+1.5\times {{10}^{11}}t)\hat{i}$

B) $\vec{B}=2\times {{10}^{-7}}\sin (1.5\times {{10}^{2}}x+0.5\times {{10}^{11}}t)\hat{j}$

C) $\vec{B}=2\times {{10}^{-7}}\sin (0.5\times {{10}^{3}}z-1.5\times {{10}^{11}}t)\hat{i}$

D) $\vec{B}=60\sin (0.5\times {{10}^{3}}x+1.5\times {{10}^{11}}t)\hat{k}$

• question_answer29) In an amplitude modulator circuit, the carrier wave is given by, $C(t)=4sin(20000\pi t)$ while modulating signal is given by, $m(t)=2sin(200\pi t)$. The values of modulation index and lower side band frequency are: [JEE Main 12-4-2019 Afternoon]

A) 0.5 and 9 kHz

B) 0.5 and 10 kHz

C) 0.3 and 9 kHz

D) 0.4 and 10 kHz

• question_answer30) In the given circuit, the charge on $4\mu F$capacitor will be: [JEE Main 12-4-2019 Afternoon]

A) $5.4\mu C$

B) $24\mu C$

C) $13.4\mu C$

D) $9.6\mu C$

• question_answer31) The molar solubility of $Cd{{(OH)}_{2}}$ is $1.84\times {{10}^{-5}}M$ in water. The expected solubility of $Cd{{(OH)}_{2}}$ in a buffer solution of pH = 12 is: [JEE Main 12-4-2019 Afternoon]

A) $6.23\times {{10}^{-11}}M$

B) $1.84\times {{10}^{-9}}M$

C) $\frac{2.49}{1.84}\times {{10}^{-9}}M$

D) $2.49\times {{10}^{-10}}M$

• question_answer32) The correct statement is : [JEE Main 12-4-2019 Afternoon]

A) leaching of bauxite using concentrated NaOH solution gives sodium aluminate and sodium silicate

B) the blistered appearance of copper during the metallurgical process is due to the evolution of $C{{O}_{2}}$

C) pig iron is obtained from cast iron

D) the Hall-Heroult process is used for the production of aluminium and iron

• question_answer33) Which one of the following is likely to give a precipitate with $AgN{{O}_{3}}$solution ? [JEE Main 12-4-2019 Afternoon]

A) ${{(C{{H}_{3}})}_{3}}CCl$

B) $CHC{{l}_{3}}$

C) $C{{H}_{2}}=CH-Cl$

D) $CC{{l}_{4}}$

• question_answer34) The compound used in the treatment of lead poisoning is : [JEE Main 12-4-2019 Afternoon]

A) EDTA

B) C is-platin

C) D-penicillamine

D) desferrioxime B

• question_answer35) A solution is prepared by dissolving 0.6 g of urea (molar mass $=60g\,mo{{l}^{-1}}$) and 1.8 g of glucose (molar mass $=180g\,mo{{l}^{-1}}$) in 100 mL of water at $27{}^\text{o}C.$The osmotic pressure of the solution is : $\left( R=0.08206\text{ }L\text{ atm }{{K}^{1}}mo{{l}^{1}} \right)$ [JEE Main 12-4-2019 Afternoon]

A) 4.92 atm

B) 1.64 atm

C) 2.46 atm

D) 8.2 atm

• question_answer36) Consider the following reactions : 'A' is: [JEE Main 12-4-2019 Afternoon]

A) $CH\equiv CH$

B) $C{{H}_{3}}-C\equiv CH$

C) $C{{H}_{2}}=C{{H}_{2}}$

D) $C{{H}_{3}}-C\equiv C-C{{H}_{3}}$

• question_answer37) What will be the major product when m-cresol is reacted with propargyl bromide $(HC\equiv C-C{{H}_{2}}Br)$ in present of ${{K}_{2}}C{{O}_{3}}$ in acetone [JEE Main 12-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer38) The INCORRECT match in the following is : [JEE Main 12-4-2019 Afternoon]

A) $\Delta {{G}^{o}}<0,K<1$

B) $\Delta {{G}^{o}}=0,K=1$

C) $\Delta {{G}^{o}}>0,K<1$

D) $\Delta {{G}^{o}}<0,K>1$

• question_answer39) The correct name of the following polymer is: [JEE Main 12-4-2019 Afternoon]

A) Polyisoprene

B) Polytert-butylene

C) Polyisobutane

D) Polyisobutylene

• question_answer40) Among the following, the energy of 2s orbital is lowest in : [JEE Main 12-4-2019 Afternoon]

A) K

B) Na

C) Li

D) H

• question_answer41) The primary pollutant that leads to photochemical smog is : [JEE Main 12-4-2019 Afternoon]

A) sulphur dioxide

B) acrolein

C) ozone

D) nitrogen oxides

• question_answer42) An 'Assertion' and a 'Reason' are given below. Choose the correct answer from the following options.

 Assertion [A] : Vinyl halides do not undergo nucleophilic substitution easily. Reason (R) : Even though the intermediate carbocation is stabilized by loosely held $\pi \text{-}$electrons, the cleavage is difficult because of strong bonding.
[JEE Main 12-4-2019 Afternoon]

A) Both [A] and (R) are wrong statements

B) Both [A] and (R) are correct statements and (R) is the correct explanation of [A]

C) Both [A] and (R) are correct statements but (R) is not the correct explanation of [A]

D) [A] is a correct statement but (R) is a wrong statement.

• question_answer43) The coordination numbers of Co and Al in $[Co(Cl){{(en)}_{2}}]Cl$ and ${{K}_{3}}[Al{{({{C}_{2}}{{O}_{4}})}_{3}}],$respectively, are :

 (en=ethane 1,2 diamine)
[JEE Main 12-4-2019 Afternoon]

A) 3 and 3

B) 6 and 6

C) 5 and 6

D) 5 and 3

• question_answer44) The IUPAC name of the following compound is : [JEE Main 12-4-2019 Afternoon]

A) 3,5-dimethyl-4-propylhept-6-en-1-yne

B) 3-methyl-4-(3-methylprop-1-enyl)-1- heptyne

C) 3-methyl-4-(1-methylprop-2-ynyl)-1- heptane

D) 3,5-dimethyl-4-propylhept-1-en-6-yne

• question_answer45) Among the following, the INCORRECT statement about colloids is : [JEE Main 12-4-2019 Afternoon]

A) They can scatter light

B) They are larger than small molecules and have high molar mass

C) The range of diameters of colloidal particles is between 1 and 1000 nm

D) The osmotic pressure of a colloidal solution is of higher order than the true solution at the same concentration

• question_answer46) In comparison to boron, beryllium has : [JEE Main 12-4-2019 Afternoon]

A) lesser nuclear charge and greater first ionisation enthalpy

B) lesser nuclear charge and lesser first ionisation enthalpy

C) greater nuclear charge and greater first ionisation enthalpy

D) greater nuclear charge and lesser first ionisation enthalpy

• question_answer47) In the following skew conformation of ethane, H'-C-C-H" dihedral angle is: [JEE Main 12-4-2019 Afternoon]

A) $120{}^\text{o}$

B) $58{}^\text{o}$

C) $149{}^\text{o}$

D) $151{}^\text{o}$

• question_answer48) $N{{O}_{2}}$required for a reaction is produced by the decomposition of ${{N}_{2}}{{O}_{5}}$in $CC{{l}_{4}}$ as per the equation $2{{N}_{2}}{{O}_{5}}(g)\to 4N{{O}_{2}}(g)+{{O}_{2}}(g).$

 The initial concentration of ${{N}_{2}}{{O}_{5}}$is 3.00 $\text{mol}\,{{\text{L}}^{-1}}$ and it is 2.75 $\text{mol}\,{{\text{L}}^{-1}}$ after 30 minutes. The rate of formation of $N{{O}_{2}}$is :
[JEE Main 12-4-2019 Afternoon]

A) $2.083\times {{10}^{3}}mol\text{ }{{L}^{1}}mi{{n}^{1}}$

B) $4.167\times {{10}^{3}}mol\text{ }{{L}^{1}}mi{{n}^{1}}$

C) $8.333\times {{10}^{3}}mol\text{ }{{L}^{1}}mi{{n}^{1}}$

D) $1.667\times {{10}^{2}}mol\text{ }{{L}^{1}}mi{{n}^{1}}$

• question_answer49) Thermal decomposition of a Mn compound (X) at 513 K results in compound $Y,Mn{{O}_{2}}$and a gaseous product. $Mn{{O}_{2}}$ reacts with NaCl and concentrated ${{H}_{2}}S{{O}_{4}}$ to give a pungent gas Z. X, Y and Z, respectively. [JEE Main 12-4-2019 Afternoon]

A) ${{K}_{2}}Mn{{O}_{4}},KMn{{O}_{4}}\text{and}\,S{{O}_{2}}$

B) ${{K}_{2}}Mn{{O}_{4}},KMn{{O}_{4}}\text{and}\,C{{l}_{2}}$

C) ${{K}_{3}}Mn{{O}_{4}},KMn{{O}_{4}}\text{and}\,C{{l}_{2}}$

D) $KMn{{O}_{4}},{{K}_{2}}Mn{{O}_{4}}\,\text{and}\,C{{l}_{2}}$

• question_answer50) 25 g of an unknown hydrocarbon upon burning produces 88 g of $C{{O}_{2}}$and 9 g of ${{H}_{2}}O.$ This unknown hydrocarbon contains. [JEE Main 12-4-2019 Afternoon]

A) 20g of carbon and 5 g of hydrogen

B) 24g of carbon and 1 g of hydrogen

C) 18g of carbon and 7 g of hydrogen

D) 22g of carbon and 3 g of hydrogen

• question_answer51) Which of the given statements is INCORRECT about glycogen ? [JEE Main 12-4-2019 Afternoon]

A) It is a straight chain polymer similar to amylose

B) Only $\alpha$-linkages are present in the molecule

C) It is present in animal cells

D) It is present in some yeast and fungi

• question_answer52) The C-C bond length is maximum in [JEE Main 12-4-2019 Afternoon]

A) graphite

B) ${{C}_{70}}$

C) diamond

D) ${{C}_{60}}$

• question_answer53) The temporary hardness of a water sample is due to compound X. Boiling this sample converts X to compound Y. X and Y, respectively, are : [JEE Main 12-4-2019 Afternoon]

A) $Ca{{(HC{{O}_{3}})}_{2}}$and$CaO$

B) $Mg{{(HC{{O}_{3}})}_{2}}$and$MgC{{O}_{3}}$

C) $Mg{{(HC{{O}_{3}})}_{2}}$and$Mg{{(OH)}_{2}}$

D) $Ca{{(HC{{O}_{3}})}_{2}}$and$Ca{{(OH)}_{2}}$

• question_answer54) The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively: [JEE Main 12-4-2019 Afternoon]

A) 1 : 2 : 4

B) 8 : 1 : 6

C) 4 : 2 : 1

D) 4 : 2 : 3

• question_answer55) Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives X as the major product. Reaction of X with $Hg{{(OAc)}_{2}}/{{H}_{2}}O$followed by $NaB{{H}_{4}}$gives Y as the major product. Y is: [JEE Main 12-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer56) In which one of the following equilibria, ${{K}_{p}}\ne {{K}_{c}}$? [JEE Main 12-4-2019 Afternoon]

A) $N{{O}_{2}}(g)+S{{O}_{2}}(g)\rightleftharpoons NO(g)+S{{O}_{3}}(g)$

B) $2HI(g)\rightleftharpoons {{H}_{2}}(g)+{{I}_{2}}(g)$

C) $2NO(g)\rightleftharpoons {{N}_{2}}(g)+{{O}_{2}}(g)$

D) $2C(s)+{{O}_{2}}(g)\rightleftharpoons 2CO(g)$

• question_answer57) Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives : [JEE Main 12-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer58) The decreasing order of electrical conductivity of the following aqueous solutions is:

 0.1 M Formic acid [A], 0.1 M Acetic acid [B] 0.1 M Benzoic acid [C]
[JEE Main 12-4-2019 Afternoon]

A) $C>B>A$

B) $A>B>C$

C) $A>C>B$

D) $C>A>B$

• question_answer59) The INCORRECT statement is : [JEE Main 12-4-2019 Afternoon]

A) Lithium is least reactive with water among the alkali metals.

B) $LiCl$ crystallises from aqueous solution as $LiCl.2{{H}_{2}}O.$

C) Lithium is the strongest reducing agent among the alkali metals.

D) $LiN{{O}_{3}}$decomposes on heating to give $LiN{{O}_{2}}$ and ${{O}_{2}}$.

• question_answer60) The pair that has similar atomic radii is : [JEE Main 12-4-2019 Afternoon]

A) Sc and Ni

B) Ti and HF

C) Mo and W

D) Mn and Re

• question_answer61) Let A, B and C be sets such that $\phi \ne A\cap B\subseteq C.$ Then which of the following statements is not true? [JEE Main 12-4-2019 Afternoon]

A) If$(A-C)\subseteq B,$then$A\subseteq B$

B) $\left( C\cup A \right)\cap \left( C\cup B \right)=C$

C) If$\left( A-B \right)\subseteq C,$then$A\subseteq C$

D) $B\cap C\ne \phi$

• question_answer62) If $^{20}{{C}_{1}}+{{\left( {{2}^{2}} \right)}^{20}}{{C}_{2}}+{{\left( {{3}^{2}} \right)}^{20}}{{C}_{3}}+.......+{{({{20}^{2}})}^{20}}{{C}_{20}}$$=A({{2}^{\beta }}),$ then the ordered pair $(A,\beta )$is equal to: [JEE Main 12-4-2019 Afternoon]

A) (420, 18)

B) (380, 19)

C) (380, 18)

D) (420, 19)

• question_answer63) A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60{}^\circ$ with the line $x+y=0.$Then an equation of the line L is: [JEE Main 12-4-2019 Afternoon]

A) $\left( \sqrt{3}+1 \right)x+\left( \sqrt{3}-1 \right)y=8\sqrt{2}$

B) $\left( \sqrt{3}-1 \right)x+\left( \sqrt{3}+1 \right)y=8\sqrt{2}$

C) $\sqrt{3}x+y=8$

D) $x+\sqrt{3}y=8$

• question_answer64) A value of $\theta \in (0,\pi /3),$for which $\left| \begin{matrix} 1+{{\cos }^{2}}\theta & {{\sin }^{2}}\theta & 4\cos 6\theta \\ {{\cos }^{2}}\theta & 1+{{\sin }^{2}}\theta & 4\cos 6\theta \\ {{\cos }^{2}}\theta & {{\sin }^{2}}\theta & 1+4\cos 6\theta \\ \end{matrix} \right|=0,$is: [JEE Main 12-4-2019 Afternoon]

A) $\frac{7\pi }{24}$

B) $\frac{\pi }{18}$

C) $\frac{\pi }{9}$

D) $\frac{7\pi }{36}$

• question_answer65) If $\left[ x \right]$denotes the greatest integer $\le x,$ then the system of linear equations $[sin\theta ]x+[-cos\theta ]$$y=0[cot\theta ]x+y=0$ [JEE Main 12-4-2019 Afternoon]

A) have infinitely many solutions if $\theta \in \left( \frac{\pi }{2},\frac{2\pi }{3} \right)\cup \left( \pi ,\frac{7\pi }{6} \right)$

B) have infinitely many solutions if$\theta \in \left( \frac{\pi }{2},\frac{2\pi }{3} \right)$and has a unique solution if$\theta \in \left( \pi ,\frac{7\pi }{6} \right)$

C) has a unique solution if $\theta \in \left( \frac{\pi }{2},\frac{2\pi }{3} \right)$and have infinitely many solutions if $\theta \in \left( \pi ,\frac{7\pi }{6} \right)$

D) has a unique solution if$\theta \in \left( \frac{\pi }{2},\frac{2\pi }{3} \right)\cup \left( \pi ,\frac{7\pi }{6} \right)$

• question_answer66) $\underset{x\to 0}{\mathop{\lim }}\,\frac{x+2\sin x}{\sqrt{{{x}^{2}}-2\sin x+1}-\sqrt{{{\sin }^{2}}x-x+1}}$is : [JEE Main 12-4-2019 Afternoon]

A) 3

B) 2

C) 6

D) 1

• question_answer67) If ${{a}_{1}},{{a}_{2}},{{a}_{3}},$..... are in A.P. such that ${{a}_{1}}+{{a}_{7}}+{{a}_{16}}=40,$then the sum of the first 15 terms of this A.P. is : [JEE Main 12-4-2019 Afternoon]

A) 200

B) 280

C) 120

D) 150

• question_answer68) The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines $\vec{r}=\left( \hat{i}+\hat{j} \right)+\lambda \left( i+2j-k \right)$and $\vec{r}=\left( \hat{i}+\hat{j} \right)+\mu \left( -\hat{i}+\hat{j}-2\hat{k} \right)$is : [JEE Main 12-4-2019 Afternoon]

A) $\sqrt{3}$

B) $\frac{1}{\sqrt{3}}$

C) $\frac{1}{3}$

D) $3$

• question_answer69) If $\alpha ,\beta$and $\gamma$are three consecutive terms of a non-constant G.P. such that the equations $\alpha {{x}^{2}}+2\beta x+\gamma =0$and ${{x}^{2}}+x1=0$ have a common root, then $\alpha (\beta +\gamma )$is equal to: [JEE Main 12-4-2019 Afternoon]

A) $\beta \gamma$

B) $0$

C) $\alpha \gamma$

D) $\alpha \beta$

• question_answer70) The term independent of x in the expansion of$\left( \frac{1}{60}-\frac{{{x}^{8}}}{81} \right).{{\left( 2{{x}^{2}}-\frac{3}{{{x}^{2}}} \right)}^{6}}$is equal to : [JEE Main 12-4-2019 Afternoon]

A) 36

B) - 108

C) - 72

D) - 36

• question_answer71) Let $\alpha \in R$and the three vectors $\vec{a}=\alpha \hat{i}+\hat{j}+3\hat{k},$ $\vec{b}=2\hat{i}+\hat{j}-\alpha \hat{k}$ and $\vec{c}=\alpha \hat{i}-2\hat{j}+3\hat{k}.$Then the set $S=\{\alpha :\vec{a},\vec{b}$and$\vec{c}$are coplanar$\}$ [JEE Main 12-4-2019 Afternoon]

A) is singleton

B) Contains exactly two numbers only one of which is positive

C) Contains exactly two positive numbers

D) is empty

• question_answer72) A value of $\alpha$such that $\int\limits_{\alpha }^{\alpha +1}{\frac{dx}{\left( x+\alpha \right)\left( x+\alpha +1 \right)}}={{\log }_{e}}\left( \frac{9}{8} \right)$is: [JEE Main 12-4-2019 Afternoon]

A) $\frac{1}{2}$

B) $2$

C) $-\frac{1}{2}$

D) $-2$

• question_answer73) A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the centroid of this triangle is: [JEE Main 12-4-2019 Afternoon]

A) $\left( \frac{1}{3},1 \right)$

B) $\left( \frac{1}{3},2 \right)$

C) $\left( 1,\frac{7}{3} \right)$

D) $\left( \frac{1}{3},\frac{5}{3} \right)$

• question_answer74) Let $\alpha \in (0,\pi /2)$ be fixed. If the integral $\int_{{}}^{{}}{\frac{\tan x+\tan \alpha }{\tan x-\tan \alpha }dx=}$$A(x)cos2\alpha +B(x)sin2\alpha +C,$ where C is a constant of integration, then the functions A(x) and B(x) are respectively : [JEE Main 12-4-2019 Afternoon]

A) $x\alpha \,\text{and lo}{{\text{g}}_{e}}|cos(x\alpha )|$

B) $x+\alpha \,\text{and lo}{{\text{g}}_{e}}|sin(x\alpha )|$

C) $x\alpha \,\text{and lo}{{\text{g}}_{e}}|sin(x\alpha )|$

D) $x+\alpha \,\text{and lo}{{\text{g}}_{e}}|sin(x+\alpha )|$

• question_answer75) A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point : [JEE Main 12-4-2019 Afternoon]

A) (3, 10)

B) (2, 3)

C) (1, 5)

D) (3, 5)

• question_answer76) For and initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is$\frac{4}{5},$ then the probability that he is unable to solve less than two problems is : [JEE Main 12-4-2019 Afternoon]

A) $\frac{316}{25}{{\left( \frac{4}{5} \right)}^{48}}$

B) $\frac{54}{5}{{\left( \frac{4}{5} \right)}^{49}}$

C) $\frac{164}{25}{{\left( \frac{1}{5} \right)}^{48}}$

D) $\frac{201}{5}{{\left( \frac{1}{5} \right)}^{49}}$

• question_answer77) The derivative of ${{\tan }^{-1}}\left( \frac{\sin x-\cos x}{\sin x+\cos x} \right),$with respect to $\frac{x}{2},$where $\left( x\in \left( 0,\frac{\pi }{2} \right) \right)$is : [JEE Main 12-4-2019 Afternoon]

A) $\frac{1}{2}$

B) $\frac{2}{3}$

C) $1$

D) $2$

• question_answer78) Let S be the set of all $\alpha \in R$such that the equation, $\cos 2x+\alpha \sin x=2\alpha -7$ has a solution. Then S is equal to : [JEE Main 12-4-2019 Afternoon]

A) [2, 6]

B) [3, 7]

C) R

D) [1, 4]

• question_answer79) The tangents to the curve $y={{\left( x-2 \right)}^{2}}-1$at its points of intersection with the line $xy=3,$ intersect at the point : [JEE Main 12-4-2019 Afternoon]

A) $\left( -\frac{5}{2},-1 \right)$

B) $\left( -\frac{5}{2},1 \right)$

C) $\left( \frac{5}{2},-1 \right)$

D) $\left( \frac{5}{2},1 \right)$

• question_answer80) A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to: [JEE Main 12-4-2019 Afternoon]

A) 25

B) 28

C) 27

D) 24

• question_answer81) The equation of a common tangent to the curves,${{y}^{2}}=16x$and $xy=4$ is : [JEE Main 12-4-2019 Afternoon]

A) $x+y+4=0$

B) $x2y+16=0$

C) $2xy+2=0$

D) $xy+4=0$

• question_answer82) Let $z\in C$ with $Im\left( z \right)=10$ and it satisfies$\frac{2z-n}{2z+n}=2i-1$for some natural number n. Then : [JEE Main 12-4-2019 Afternoon]

A) $n=20$ and $Re\left( z \right)=10$

B) $n=20$ and $Re\left( z \right)=10$

C) $n=40$ and$Re\left( z \right)=-10$

D) $n=40$ and$Re\left( z \right)=10$

• question_answer83) The general solution of the differential equation $\left( {{y}^{2}}{{x}^{3}} \right)dxxydy=0(x\ne 0)$ is:

 (where c is a constant of integration)
[JEE Main 12-4-2019 Afternoon]

A) ${{y}^{2}}+2{{x}^{3}}+c{{x}^{2}}=0$

B) ${{y}^{2}}+2{{x}^{2}}+c{{x}^{3}}=0$

C) ${{y}^{2}}2{{x}^{3}}+c{{x}^{2}}=0$

D) ${{y}^{2}}2{{x}^{2}}+c{{x}^{3}}=0$

• question_answer84) A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs.12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is : [JEE Main 12-4-2019 Afternoon]

A) $2gain$

B) $\frac{1}{2}loss$

C) $\frac{1}{4}loss$

D) $\frac{1}{2}gain$

• question_answer85) Let $f\left( x \right)=5\left| x2 \right|$ and $g(x)=|x+1|,x\in R.$ If f(x) attains maximum value at a and g(x) attains minimum value at $\beta$ then $\underset{x\to -\alpha \beta }{\mathop{\lim }}\,\frac{\left( x-1 \right)\left( {{x}^{2}}-5x+6 \right)}{{{x}^{2}}-6x+8}$is equal to : [JEE Main 12-4-2019 Afternoon]

A) 1/2

B) -3/2

C) 3/2

D) -1/2

• question_answer86) The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be $45{}^\circ$from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be $30{}^\circ ,$then the distance (in m) of the foot of the tower from the point A is: [JEE Main 12-4-2019 Afternoon]

A) $15\left( 3-\sqrt{3} \right)$

B) $15\left( 3+\sqrt{3} \right)$

C) $15\left( 1+\sqrt{3} \right)$

D) $15\left( 5-\sqrt{3} \right)$

• question_answer87) The Boolean expression $\tilde{\ }(p\Rightarrow (\tilde{\ }q))$is equivalent to : [JEE Main 12-4-2019 Afternoon]

A) $(\tilde{\ }p)\Rightarrow q$

B) $p\vee q$

C) $q\Rightarrow \tilde{\ }p$

D) $p\wedge q$

• question_answer88) A plane which bisects the angle between the two given planes $2xy+2z4=0$and $x+2y+2z2=0,$ passes through the point: [JEE Main 12-4-2019 Afternoon]

A) (2, 4, 1)

B) (2, -4, 1)

C) (1, 4, -1)

D) (1, -4, 1)

• question_answer89) If the area (in sq. units) bounded by the parabola ${{y}^{2}}=4\lambda x$ and the line $y=\lambda x,\lambda >0,$is $\frac{1}{9},$ then $\lambda$ is equal to : [JEE Main 12-4-2019 Afternoon]

A) 24

B) 48

C) $4\sqrt{3}$

D) $2\sqrt{6}$

• question_answer90) An ellipse, with foci at (0, 2) and (0, -2) and minor axis of length 4, passes through which of the following points? [JEE Main 12-4-2019 Afternoon]

A) $(1,2\sqrt{2})$

B) $(2,\sqrt{2})$

C) $(2,2\sqrt{2})$

D) $(\sqrt{2},2)$